WorkKinetic Energy Theorem

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Work-Kinetic Energy Theorem

• Work
• Work-Kinetic Energy Theorem
• Conservation of Energy
• Power

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Reading Question
When is the next exam?

• Next Wednesday, October 26
• My wifes birthday, Thursday, October 27
• 3. Next Friday, October 28
• 4. Next Monday, November 1
• 5. Wednesday, November 3

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Reading Question
When is the next exam?

• Next Wednesday, October 26
• My wifes birthday, Thursday, October 27
• 3. Next Friday, October 28
• 4. Next Monday, November 1
• 5. Wednesday, November 3

4
Reading Question
A particle moving along the x-axis experiences
the force shown in the graph. If the particle has
4.0 J of kinetic energy as it passes x 0 m,
what is its kinetic energy when it reaches x 4
m?

• 1. 2.0 J
• 2. 0.0 J
• 3. 2.0 J
• 4. 4.0 J
• 6.0 J
• 8.0 J

5
Reading Question
A particle moving along the x-axis experiences
the force shown in the graph. If the particle has
4.0 J of kinetic energy as it passes x 0 m,
what is its kinetic energy when it reaches x 4
m?

• 1. 2.0 J
• 2. 0.0 J
• 3. 2.0 J
• 4. 4.0 J
• 6.0 J
• 8.0 J

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Reading Question
A particle moves along the x-axis with the
potential energy shown. The force on the particle
when it is at x 4 m is
1. 4 N. 2. 2 N. 3. 1 N. 4. 1 N. 5. 2 N.
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Reading Question
A particle moves along the x-axis with the
potential energy shown. The force on the particle
when it is at x 4 m is
1. 4 N. 2. 2 N. 3. 1 N. 4. 1 N. 5. 2 N.
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Reading Question
A child at the playground slides down a pole at
constant speed. This is a situation in which
1. U Eth. Emech is conserved. 2. U K. Emech
is not conserved but Esys is. 3. K Eth. Emech
is not conserved but Esys is. 4. U Eth. Emech
is not conserved but Esys is. 5. U Wext.
Neither Emech nor Esys are conserved.
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Reading Question
A child at the playground slides down a pole at
constant speed. This is a situation in which
1. U Eth. Emech is conserved. 2. U K. Emech
is not conserved but Esys is. 3. K Eth. Emech
is not conserved but Esys is. 4. U Eth. Emech
is not conserved but Esys is. 5. U Wext.
Neither Emech nor Esys are conserved.
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Reading Question
Four students run up the stairs in the time
shown. Rank in order, from largest to smallest,
their power outputs Pa to Pd.
1. Pb gt Pa Pc gt Pd 2. Pd gt Pa Pb gt Pc 3.
Pd gt Pb gt Pa gt Pc 4. Pb gt Pa gt Pc gt Pd 5. Pc
gt Pb Pa gt Pd
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Reading Question
Four students run up the stairs in the time
shown. Rank in order, from largest to smallest,
their power outputs Pa to Pd.
1. Pb gt Pa Pc gt Pd 2. Pd gt Pa Pb gt Pc 3.
Pd gt Pb gt Pa gt Pc 4. Pb gt Pa gt Pc gt Pd 5. Pc
gt Pb Pa gt Pd
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Work-Kinetic Energy Theorem
Energy Model
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Work-Kinetic Energy Theorem
Energy Model
W gt 0 The environment does work on the system
and the systems energy increases.
W lt 0 The system does work on the environment
and the systems energy decreases.
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Work-Kinetic Energy Theorem
Work-Energy Theorem The change in kinetic
energy is equal to the net work on the object
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Work-Kinetic Energy Theorem
The definition for work is
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Work-Kinetic Energy Theorem
An airline passenger pulls her wheeled suitcase,
exerting a 60 N force at a 350 angle to the
horizontal. How much work does she do to pull
the suitcase 45 m from the taxi to the check-in
counter?
The force and angle between the force and
displacement are constant so
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Work-Kinetic Energy Theorem
A 0.10 kg cube is launched by a spring with a
spring constant of 20 N/m. What is the speed of
the cube just as it leaves the spring if it
travels 20 cm before coming to rest. Assume the
surface is rough and the coefficient of friction
is 0.10?

• Draw a physical picture for the two different
  times (before and after).

• Label the picture with what you know.

• Draw a free body diagram.

• Write the Work-Kinetic Energy Theorem.

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Work-Kinetic Energy Theorem
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Student Workbook
The first question to ask is the force constant?
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Student Workbook
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Student Workbook
The kinetic energy of the two carts is the same.
The change in kinetic energy is equal to the net
work on the cart and the net work is the same on
both carts.
Zero, the work depends on the angle between the
force (tension in string) and the displacement
(tangent to the circle) and this angle is 90
degrees.
Yes, the net work is zero and the change in
kinetic energy is zero.
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Class Question
Which force does the most work?
1. The 6 N force. 2. The 8 N force. 3. The 10 N
force. 4. They all do the same amount of work.
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Class Question
Which force does the most work?
1. The 6 N force. 2. The 8 N force. 3. The 10 N
force. 4. They all do the same amount of work.
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Class Question
A crane lowers a steel girder into place at a
construction site. The girder moves with constant
speed. Consider the work Wg done by gravity and
the work WT done by the tension in the cable.
Which of the following is correct?
1. Wg is positive and WT is positive. 2. Wg is
negative and WT is negative. 3. Wg is positive
and WT is negative. 4. Wg and WT are both
zero. 5. Wg is negative and WT is positive.
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Class Question
A crane lowers a steel girder into place at a
construction site. The girder moves with constant
speed. Consider the work Wg done by gravity and
the work WT done by the tension in the cable.
Which of the following is correct?
1. Wg is positive and WT is positive. 2. Wg is
negative and WT is negative. 3. Wg is positive
and WT is negative. 4. Wg and WT are both
zero. 5. Wg is negative and WT is positive.
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Work-Kinetic Energy Theorem
Work with a Variable Force
What other two forms can we use for the work?
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Work-Kinetic Energy Theorem
Work done by a variable force
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Student Workbook
(1/2)6m10N30Nm
10Nm-15Nm -5Nm
30Nm
-5Nm
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Student Workbook
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Student Workbook
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Class Question
A particle moving along the x-axis experiences
the force shown in the graph. If the particle has
4.0 J of kinetic energy as it passes x 0 m,
what is its kinetic energy when it reaches x 4
m?

• 1. 2.0 J
• 2. 0.0 J
• 3. 2.0 J
• 4. 5.0 J
• 8.0 J
• 10 J

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Class Question
A particle moving along the x-axis experiences
the force shown in the graph. If the particle has
2.0 J of kinetic energy as it passes x 0 m,
what is its kinetic energy when it reaches x 4
m?

• 1. 2.0 J
• 2. 0.0 J
• 3. 2.0 J
• 4. 5.0 J
• 8.0 J
• 10 J

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Work-Kinetic Energy Theorem
Conservative and Nonconservative Forces
For a conservative force the work is independent
of path.
For a nonconservative force the work is dependent
of path.
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Student Workbook
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Work-Kinetic Energy Theorem
Finding force from potential energy
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Work-Kinetic Energy Theorem
Finding force from potential energy
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Work-Kinetic Energy Theorem
Thermal Energy
Kinetic and potential energy at the microscopic
level
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Work-Kinetic Energy Theorem
Dissipative forces
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Work-Kinetic Energy Theorem
Conservation of energy
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Work-Kinetic Energy Theorem
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Work-Kinetic Energy Theorem
Example 11.14
A cube is attached to a spring that is attached
to the wall. The cube is at rest and the spring
is at its equilibrium position when a 100 N force
is applied to the cube by a string . What is the
cubes velocity after it has moved 0.50m over a
rough surface with m 0.30?
from this equation you can find v.
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Student Workbook
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Work-Kinetic Energy Theorem
Movers are pushing a 78.0-kg trunk at 0.71 m/s
when they encounter a 2.25 m-long stretch of
floor where the coefficient of kinetic friction
is 0.295. If they push with a steady force F
220 N, determine the speed of the trunk at the
speed of the end of the stretch.
Using the work-energy theorem
First calculate the work is the net force
constant?
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Student Workbook
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Work-Kinetic Energy Theorem
Power
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Work-Kinetic Energy Theorem
Power
Examples of power